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Valuation (logic)

In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema.

Version
v1 · 2026-09-28 · History
Domain-specific #
12751
Domain group
Formal Sciences
Origin domain
Mathematics
Subdomains
Mathematical Logic, Model Theory → Mathematics

Core Idea

Valuation (logic) is treated here as the recurring mathematicslogicstatistics identity summarized by this source-grounded definition: In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema. In logic and model theory, a valuation can be. In propositional logic, an assignment of truth values to propositional variables, with a corresponding assignment of truth values to all propositional formulas with those variables. In first-order logic and higher-order logics, a structure, (the interpretation) and the corresponding assignment of a truth value to each sentence in the language.

Scope of Application

  • Mathematical logic. In first-order logic, a language consists of a collection of constant symbols, a collection of function symbols, and a collection of relation symbols.

  • Mathematical logic. A structure consists of a set (domain of discourse) that determines the range of the quantifiers, along with interpretations of the constant, function, and relation symbols in the language.

  • Notation. If v is a valuation, that is, a mapping from the atoms to the set { t, f } , then the double-bracket notation is commonly used to denote a valuation; that is.

  • Documented setting. The interpretation must be a homomorphism, while valuation is simply a function.

  • Mathematical logic. In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema.

Clarity

A clear use of Valuation (logic) names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema.

Manages Complexity

Valuation (logic) compresses multiple mathematicslogicstatistics details into a stable diagnostic relation. The source shows both the central mechanism—a structure consists of a set (domain of discourse) that determines the range of the quantifiers, along with interpretations of the constant, function, and relation symbols in the language.—and the practical consequence—this assignment can be uniquely extended to an assignment of truth values to all propositional formulas.

Abstract Reasoning

  1. Type the carrier. Identify the mathematicslogicstatistics entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema.
  3. Check operation and conditions. In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema.
  4. Demand recognition evidence.

Knowledge Transfer

Within the home domain. Knowledge about Valuation (logic) transfers literally when a new case preserves the same carrier type, relation, and recognition test. In first-order logic, a language consists of a collection of constant symbols, a collection of function symbols, and a collection of relation symbols. A structure consists of a set (domain of discourse) that determines the range of the quantifiers, along with interpretations of the constant, function, and relation symbols in the language. Beyond the home domain. No canonical parent is asserted for Valuation (logic).

Relationships to Other Abstractions

Local relationship map for Valuation (logic)Parents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Valuation (logic)DOMAINPrime abstraction: Function (Mapping) — is a kind ofFunction(Mapping)PRIME

Current abstraction Valuation (logic) Domain-specific

Parents (1) — more general patterns this builds on

  • Valuation (logic) is a kind of Function (Mapping) Prime

    A logical valuation is an assignment mapping formulas or sentences to truth values under a schema; it is not itself a logic system and is unrelated to Omega-logic.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

Valuation (logic) sits in a crowded region of the domain-specific corpus (25th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Formal Logic & Language Constructs (20 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08